Brief Communication

UFBoot2: Improving the Ultrafast Bootstrap Approximation

Diep Thi Hoang1,§ , Olga Chernomor2,§, Arndt von Haeseler2,3, Bui Quang Minh2,* and Le Sy

Vinh1,*

1University of Engineering and Technology, Vietnam National University, Hanoi, Vietnam,

2Center for Integrative Bioinformatics Vienna, Max F. Perutz Laboratories, University of

Vienna, Medical University Vienna, Vienna, Austria,

3Bioinformatics and Computational Biology, Faculty of Computer Science, University of

Vienna, Vienna, Austria.

*To whom correspondence should be addressed.

§ Shared first authors

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Abstract

The standard bootstrap (SBS), despite being computationally intensive, is widely used in

maximum likelihood phylogenetic analyses. We recently proposed the ultrafast bootstrap

approximation (UFBoot) to reduce computing time while achieving more unbiased branch

supports than SBS under mild model violations. UFBoot has been steadily adopted as an

efficient alternative to SBS and other bootstrap approaches.

Here, we present UFBoot2, which substantially accelerates UFBoot and reduces the risk of

overestimating branch supports due to polytomies or severe model violations. Additionally,

UFBoot2 provides suitable bootstrap resampling strategies for phylogenomic data. UFBoot2

is 778 and 8.4 times (median) faster than SBS and RAxML rapid bootstrap on tested datasets,

respectively. UFBoot2 is implemented in the IQ-TREE software package version 1.6 and

freely available at http://www.iqtree.org.

Keywords: phylogenetic inference, ultrafast bootstrap, maximum likelihood, model violation

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Standard nonparametric bootstrap (SBS) (Efron 1979; Felsenstein 1985) is widely used in

maximum likelihood (ML) phylogenetic analyses to estimate branch supports of a

phylogenetic tree inferred from a multiple sequence alignment (MSA). To achieve this, SBS

generates a large number of resampled MSAs and reconstructs an ML-tree for each

bootstrapped MSA. The resulting bootstrap ML trees are then used either to compute branch

supports for the ML-tree reconstructed from the original MSA or to build a consensus tree

with support values.

Although fast ML-tree search algorithms exist for large datasets (Vinh and von Haeseler

2004; Stamatakis 2006; Guindon et al. 2010; Nguyen et al. 2015) SBS is still very

computationally intensive. To improve computing time rapid bootstrap (RBS; Stamatakis et

al. 2008) and the ultrafast bootstrap (UFBoot; Minh et al. 2013) were developed. While RBS

resembles the conservative behavior of SBS (i.e., underestimating branch supports), UFBoot

provides relatively unbiased bootstrap estimates under mild model misspecifications.

The key idea behind UFBoot is to keep trees encountered during the ML-tree search for the

original MSA and to use them to evaluate the quality (likelihood) of the bootstrap MSAs. To

speed up likelihood computation even further for bootstrap MSAs, IQ-TREE employed the

resampling estimated log-likelihood (RELL) strategy (Kishino et al. 1990). For each

bootstrap MSA the tree with the highest RELL score (RELL-tree) represents the ML-

bootstrap tree. Contrary to SBS, UFBoot does not further ML optimize this tree. The

discrepancy in branch supports between UFBoot and SBS emerges as bootstrap trees inferred

by UFBoot and SBS might be different.

Here, we present UFBoot2 that substantially speeds up UFBoot and reduces the risk for

overestimated branch support due to polytomies or severe model violations. We will also

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discuss several resampling strategies for phylogenomic data recently implemented in

UFBoot2.

Accelerating UFBoot

The likelihood computation is the major runtime bottleneck of all ML software because it lies

at the core of all analyses. The pruning algorithm (Felsenstein 1981) efficiently computes the

likelihood of phylogenetic trees, but still does not scale well for large data sets. Therefore, we

adopted a modification to Felsenstein’s algorithm, first introduced in RAxML. The

modification exploits the reversible property of models of sequence evolution typically used

in phylogenetic analysis, which led to a theoretical speedup of 4 (for DNA) or 20 (for protein

data) when estimating branch lengths. Moreover, we employed the SIMD (single instruction,

multiple data) feature to concurrently compute the likelihood of two MSA-sites with

streaming SIMD extensions or four MSA-sites with advanced vector extensions, thus leading

to a theoretical speedup of two or four compared with a non-SIMD implementation. IQ-

TREE code was further optimized to avoid redundant computations.

Our benchmark on 70 DNA and 45 protein MSAs showed that UFBoot2 achieved a median

speedup of 2.4 times (maximum: 77.3) compared with UFBoot version 0.9.6 (released on

October 20, 2013).

Correction for polytomies

Polytomies refer to multifurcating nodes in the tree that cannot be resolved due to low

phylogenetic signal in the data. However, phylogenetic reconstruction always assumes

strictly bifurcating trees. When resolving polytomies there might be multiple equivalently

optimal bifurcating trees. As UFBoot saves only a single optimal bifurcating tree for each

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bootstrap MSA, it might cause over-optimistic bootstrap supports for short branches

(Simmons and Norton 2014).

To correct for this shortcoming UFBoot2 implemented the following technique. Instead of

assigning the bootstrap tree with the highest RELL for each bootstrap MSA, UFBoot2 will

randomly select trees encountered during tree search, whose RELL scores are less than 𝜀!""#

(default: 0.5) away from the highest RELL.

It was shown with a star tree simulation (Simmons and Norton 2014) that SBS and RBS

sometimes led to false positives (bootstrap supports ≥ 95% for non-existing branches),

whereas with this technique UFBoot2 never supported such branches (support values ≤

88%). Therefore, the above technique prevents over-optimistic supports.

Reducing the impact of model violations

Minh et al. (2013) showed that severe model violations inflate UFBoot support values. To

resolve this issue UFBoot2 provides an option to conduct an additional step once the tree

search on the original MSA is completed. Here, the best RELL-trees are further optimized

using a hill-climbing nearest-neighbor interchange (NNI) search based directly on the

corresponding bootstrap MSA. Thus, this extra step operates like SBS, but with a quick tree

search to save time. Bootstrap supports are then summarized from the resulting corrected

bootstrap trees. In the following, we called this UFBoot2+NNI.

We repeated the PANDIT simulations in (Minh et al. 2013) to compare the accuracy of

UFBoot2 and UFBoot2+NNI with SBS (1000 replicates using IQ-TREE) and RBS (RAxML

bootstopping criterion). Figure 1 shows the results. If the sequence evolution model used to

infer the ML-tree agrees with the model used for simulations, then SBS, RBS and

UFBoot2+NNI underestimated branch supports, the latter to a lower degree (Figure 1A;

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curves above the diagonal), whereas UFBoot2 obtained almost unbiased branch supports

(Figure 1A; curve close to the diagonal). Severe model violations do not influence SBS

(Figure 1B; RBS not shown because RAxML does not support simpler model). However,

UFBoot2 (like UFBoot) overestimated the branch supports (Figure 1B; curve below the

diagonal), while UFBoot2+NNI only slightly underestimated the bootstrap values (Figure

1B; curve closest to the diagonal).

In terms of computation times, UFBoot2 and UFBoot2+NNI showed a median speedup of

778 (range: 200-1,848) and 424 (range: 233-749) compared with SBS, respectively.

Compared with RBS, UFBoot2 and UFBoot2+NNI are 8.4 (range: 1.5-51.2) and 5.0 (range:

0.8-32.6) times faster, respectively. Therefore, UFBoot2+NNI is two times (median) slower

than UFBoot2.

We conclude that UFBoot2 and UFBoot2+NNI are fast alternatives to other bootstrap

approaches. Users are advised to apply model violation detection methods (e.g., Goldman

1993; Weiss and von Haeseler 2003; Nguyen et al. 2011) before bootstrap analyses.

UFBoot2+NNI should be applied if model violations are present in the data set at hand.

Resampling strategies for phylogenomic data

Recent phylogenetic analyses are typically based on multiple genes to infer the species tree,

the so-called phylogenomics. To facilitate phylogenomic analysis, UFBoot2 implements

three bootstrap resampling strategies: (i) resampling MSA-sites within partitions (denoted as

MSA-site resampling), (ii) resampling genes instead of MSA-sites (gene-resampling) and (iii)

resampling genes and subsequently resamples MSA-sites within each gene (gene-site

resampling) (Gadagkar et al. 2005). Strategy (i) preserves the number of MSA-sites for all

genes in the bootstrap MSAs, whereas strategies (ii) and (iii) will lead to different number of

sites in the bootstrap MSAs.

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To investigate the impact of the three resampling strategies, we reanalyzed the metazoan data

with 21 species, 225 genes and a total of 171,077 amino-acid sites (Salichos and Rokas

2013). Figure 2 shows the ML tree inferred under edge-unlinked partition model (Chernomor

et al. 2016), which allows separate sets of branch lengths across partitions. The tree replicates

previous results (Salichos and Rokas 2013) and shows the Protostomia clade (Telford et al.

2015). However, discrepancies between resampling strategies are observed: while MSA-site

and gene-resamplings obtained high supports (>95%) for branches along the backbone of the

tree (Figure 2; bold lines), lower supports (80%) were estimated by gene-site resampling.

By further examining 14 other empirical data sets (Bouchenak-Khelladi et al. 2008; Fabre et

al. 2009; van der Linde et al. 2010; Stamatakis and Alachiotis 2010; Pyron et al. 2011;

Nyakatura and Bininda-Emonds 2012; Springer et al. 2012; Hinchliff and Roalson 2013;

Salichos and Rokas 2013; Dell’Ampio et al. 2014), we observed more discrepancies between

resampling strategies (data not shown). Exceptionally for some data sets a number of

branches showed almost no support (≤10%) for one resampling but high supports (≥95%) for

the other two resampling strategies. However, there is no tendency towards systematically

lower supports obtained by one resampling strategy.

Taking into account the above findings, we recommend to apply all alternative resampling

strategies. If similar bootstrap supports are obtained, then one can be more confident about

the results.

Conclusions

UFBoot2 significantly improves speed and accuracy of bootstrap values compared to

UFBoot. It also offers new functionalities in the presence of model violations and in its

applicability to phylogenomic data. In general, since SBS, RBS and UFBoot2+NNI share a

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disadvantage of being conservative, more research is necessary to understand the different

biases introduced by the available phylogenetic bootstrap estimation methods.

Acknowledgment

The authors thank Stephen Crotty for comments on the manuscript. This work was supported

by Vietnam National Foundation for Science and Technology Development (102.01-

2013.04). AVH, BQM, and OC were supported by the Austrian Science Fund - FWF (grant

no. I-2805-B29 and I-1824-B22).

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Figure captions

Figure 1. Accuracy of the standard bootstrap (SBS), RAxML rapid bootstrap (RBS), ultrafast

bootstrap (UFBoot2) and UFBoot2+NNI for (A) correctly specified models and (B) severely

misspecified models. Curves above the diagonal indicate underestimation of branch supports

whereas curves below the diagonal indicate overestimation.

Figure 2. Maximum likelihood tree inferred under the edge-unlinked partition model.

Numbers attached to the branches show the UFBoot2 bootstrap supports using MSA-site,

gene, and gene MSA-site resampling strategies (omitted when all three supports are 100%).

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Figure 1

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Figure 2

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